def test_takagi_factorization_real_neg_imag_neg(rank, dtype):
a = get_random_complex_symmetric_matrices(10, rank, dtype)
a = sm.to_complex(a.real * -1, a.imag * -1)
eigenvalues, s = sm.takagi_eig(a)
assert_sds_equals_a(s, eigenvalues, a)
def assert_sds_equals_a(s, eigenvalues, a, atol=1e-5, rtol=1e-5):
diagonal = torch.diag_embed(eigenvalues)
diagonal = sm.to_complex(diagonal, torch.zeros_like(diagonal))
np.testing.assert_allclose(
a,
s.conj() @ diagonal @ s.conj().transpose(-1, -2),
atol=atol,
rtol=rtol)
def test_takagi_factorization_imag_identity(rank, dtype):
a = sm.identity_like(get_random_complex_symmetric_matrices(
10, rank, dtype))
a = sm.to_complex(a.imag, a.real)
eigenvalues, s = sm.takagi_eig(a)
assert_sds_equals_a(s, eigenvalues, a)
def test_takagi_factorization_idem_takagi_fact():
real_a = torch.Tensor([[[0.222662581850819, 0.98644223215106],
[0.98644223215106, 0.27907583542894]]])
imag_a = torch.Tensor([[[0.204990135642257, 1.28603437847092],
[1.28603437847092, 1.18098457998164]]])
a = sm.to_complex(real_a, imag_a)
eigenvalues, s = sm.takagi_eig(a)
assert_sds_equals_a(s, eigenvalues, a)